This invention relates generally to anechoic chambers of the type used for measuring the amount of electromagnetic radiation emitted by electrical equipment under test and more specifically to a method for optimizing the low-frequency design of pyramid cone absorbers employed in such chambers. The Federal Communications Commission (FCC) imposes limits on the amount of electromagnetic radiation emitted by electrical equipment sold in the United States. As a result, such electrical equipment must be tested to insure compliance with the FCC regulations. These tests are required to be performed over a frequency range of 30-1000 MHz in an open field environment. The emitted electromagnetic radiation at specified test frequencies within this range must be less than a limit value. Open field testing is not ideal because the tests are not repeatable due to changing factors in the environment itself. Factors such as humidity, weather conditions, soil conductivity, and proximity of the test site to buildings, trees, and commercial broadcast radio stations have the effect of altering the conductivity of the test environment and interrupting test scheduling. In view of these problems with open field testing, the FCC permits tests to be conducted in anechoic chambers so long as the chamber test results can be correlated with open field measurements.
An understanding of microwave absorbing materials and their use in anechoic chambers may be had with reference to S. Galagan, Understanding Microwave Absorbing Materials and Anechoic Chambers--Parts 1-4, Microwaves, Vol. 8, No. 12 and Vol. 9, Nos. 1, 4, and 5 (December, 1969, and January, April, May, 1970). At the high-frequency end (typically 300-1000 MHZ) of the test frequency range, tests have generally been performed inside anechoic chambers. At these high frequencies the skin-depth of the incident electromagnetic radiation is very small compared to the thickness of the backing absorber lining the metal walls of the anechoic chamber. Therefore, the electromagnetic radiation is mostly absorbed in the tapered section of the pyramidal absorbing structure. This results in only a very small portion of the incident electromagnetic radiation interacting with and being reflected from the metal walls of the anechoic chamber. Also, at these high frequencies, the wavelength of the incident electromagnetic radiation is small compared to the dimensions of the pyramidal absorber structure. Thus, the incident electromagnetic radiation sees the fine structure, or each individual shape in the absorber array. Through the use of geometric optics analysis, it can be shown that the incident electromagnetic radiation is bounced off the tapered section of a pyramidal absorber several times, propagating both in and out of the absorber structure. A certain amount of the incident electromagnetic radiation is absorbed during each bounce, so that only a very small amount of energy remains after the incident electromagnetic radiation has exited the absorber structure, as illustrated in FIG. 1, thereby resulting in a low coefficient of reflection.
The poor performance of anechoic chambers at the low-frequency end (typically 30-300 MHZ) of the test frequency range can be explained using the same analysis as recited above. At these low frequencies, the skin depth of the incident electromagnetic radiation is large compared to the dimensions of the pyramidal absorber employed in the anechoic chamber. As a result, the incident electromagnetic radiation passes easily through the tapered section of the pyramidal absorber into the backing absorber and onto the metal wall of the anechoic chamber. Little or none of the incident electromagnetic radiation is absorbed before it interacts with the metal wall, thereby resulting in a high coefficient of reflection. At the low-frequency end of the test frequency range, the wavelength is large compared to the dimensions of the pyramidal absorbers. The incident electromagnetic radiation does not see the fine structure of the pyramidal absorbers, but sees an effective or averaged layer of absorber. Therefore, the incident electromagnetic radiation bounces only once off the effective layer, as illustrated in FIG. 2, resulting in the absorption of much less energy than in the high frequency case and in large reflections off the walls of the anechoic chamber.
It is thus the principal object of the present invention to accurately model and optimize the low-frequency properties of pyramidal cone absorbing structures as an aid in designing such structures for use in anechoic chambers. This object is accomplished by providing a process for optimizing the coefficient of reflection of a pyramidal cone absorbing structure over a desired frequency range.
To analyze the low frequency response of the anechoic chamber walls, the pyramidal absorber structure is equated to an effective absorbing layer. Maxwell's equations are separated into a perpendicular polarization and a parallel polarization set of equations. With these two sets of equations, the effective permittivity and permeability for both polarizations of the equivalent layer can be determined.
The effective material properties .epsilon..sub.eff (z) and .mu..sub.eff (z) are functions of z, the coordinate penetrating into the pyramidal absorbing structure. This coordinate dependence on the effective material properties is due to the geometry of the pyramidal absorbing structure. That is, the cross-section of the structure changes as z changes. These effective properties are also functions of the transverse and longitudinal material properties of the effective layer. The transverse and longitudinal material properties are also a result of the geometry of the pyramidal absorbing structure, and themselves are functions of the coordinate z.
The longitudinal and transverse material properties are obtained through a technique known as homogenization. Homogenization allows separation of the average field values from the microstructure of the fields. It is then possible to examine only the average field values. The averaged fields satisfy Maxwell's equations in a medium where the properties of the medium are replaced by homogenized or averaged values.
Once Maxwell's equations are broken into the two polarizations, each set of equations is arranged in such a manner that they are reduced to the classical transmission line equations. With the equations arranged in this manner, an expression for a general coefficient of reflection can be obtained, and from this general coefficient of reflection, the expression representing the coefficient of reflection for the absorbing structure is obtained.
The process, which is most efficiently performed using a computer, involves an initial choice of complex permittivity values at the desired frequencies. Using this initial value of complex permittivity, the expression representing the coefficient of reflection (reflection coefficient) is evaluated. If not as low as desired, the coefficient of reflection can be reduced by increasing the values of complex permittivity. This iterative process is followed until no further improvement in the computed value of the maximum coefficient of reflection over a specified frequency range is obtained. At this point, the pyramidal absorber is performing at its optimum for a given set of physical dimensions of the individual pyramidal cones comprising the pyramidal cone absorber structure. The process of the present invention may also be similarly employed to optimize the coefficient of reflection of the absorber structure for a fixed set of complex permittivity values by altering the pyramidal cone dimensions while maintaining the total length of the pyramidal cone plus backing layer thickness as a constant.